Skip to main content

Full text of "Analytical Mechanics"

See other formats

17.  Particle.—A body whose dimensions are negligible is called a particle.   In a problem any body may be considered as a particle so long as it does not tend to rotate.    Even when the body rotates it may be considered as a particle if its rotation does not enter into the problem.    For instance, in discussing the motion of the earth in its orbit the earth is considered as a particle, because its rotation about its axis does not enter into the discussion.
18.  Degrees of Freedom.—The number of independent ways in which a body can move is called the number of (Icynrs of freedom of its motion.   It equals the number of coordinates which are necessary in order to specify completely (he position of the body.   A free particle can move in three independent directions, that is, along the three axes of a system of rectangular coordinates, therefore it has three degrees of freedom.   When the particle is constrained to move in a plane its freedom is reduced to two degrees, because it can move only in two independent directions.    When it "is constrained to move in a straight line it has only one degree of freedom.
19.  Force.—-While considering the motion or the equilibrium of a body our attention is claimed not only by that body but also by others which act upon it.   In order to insure concentration of attention problems in Dynamics arc* simplified in the following manner.   All bodies are eliminated, except the one the motion of which is being discussed, and their actions upon the latter are represented by certain vector magnitudes known as forces.  As an illustration consider